Heat Equation Derivation

Organized by textbook: learncheme.com/
Derives the heat equation using an energy balance on a differential control volume.
Made by faculty at the University of Colorado Boulder Department of Chemical and Biological Engineering.
Check out our Heat Transfer playlist: • Heat Transfer
Check out our website for interactive heat transfer simulations: www.learncheme....

[@mahammadsadigov2818]

Even though it was passed through 10 years from the day the video broadcasted, I am watching it and beholden to the person who elucidated the heat equation derivation in an elaborate manner.

[@knutejay]

thank you!!

[@DarkSlayerphlc]

I said it 5 years ago and i repeat now.... I learned more from this video that all my years in college... that tells something...

[@bim1537]

I wonder, what kind of people disliking this video, it's very helpful,
Thank you sir, you're da MVP

[@MrAmgadHasan]

Thank you for this amazing explanation. As for energy "generation", we can use the term "heat generation" as it is more suitable.

[@joeed01]

Best explanation I've seen online so far! Thanks!

[@alvarozerkowski3706]

Oh my God! What a great and straightforward explanation!! Tks!!

[@jrcr1993]

Thank you a lot for this amazing video. You've given me insight like no other.

[@Ikarhxc]

I'm in love with the way you explain and also the screen casting, which app are you using? Pretty interesting! Much love for the teachers behind this you are true heroes.

[@keenanaugustus1547]

Hi,
I'm having trouble understanding how you got the equation at 9:56 from plugging in "flow of E in and out" for qx. it looks like extra terms were added. It seems like i am missing something, can you help me out? Thanks

[@wandersonFBraz]

7:36 isn't that Cv? for its Internal energy and not Enthalpy?

[@hnn-d9o]

thanks man, it was helpful to solve my homework for heat transfer

[@natyalim]

Absolutely magnificent video! Thanks! Never understood this until now. :)

[@dimitarstoyanov9932]

Great work, mate. This is extremely helpful video. Good job.

[@nikan4now]

Good demonstration. Thanks. This is only for conduction though!

[@zaidshaikh2180]

LearnChemE Hello. I have a minor confusion about temperature. On the right hand side, I see dT/dt. Here, what does T represent? It is the temperature of what? I know temperature varies according to the coordinates and hence we don't have uniform temperature in this box. But then, why would we have a temperature that varies with time?

[@gl00n27]

In this case we do not have the temperature change with time, because the steady state conduction is a condition for the deduction. Anyway, transient conduction is explained in the next lessons.

[@joacollou]

When you use Taylor Series for the heat flux at (x + dx) and neglect the higher order terms, do you get an exact result (assuming k is constant)? And, if so, is it because of the linear nature that arises from Fourier's law?
Thanks!

[@chandrachudmishra2671]

Yes

[@274152]

is "q" a rate (heat flux) or a heat quantity (energy)?

[@rafaanimir8820]

This channel is really amazing, thumbs up (y)

[@bhaveshohal3390]

Great video sir...

[@vinr1187]

Good Mate. Can you do a similar one each for two dimensional and three dimensional. Thanks

[@parthdodia2553]

thank you soo much....you made it easy to understand

[@ak5ogaming99]

Write answer equation of heat flow in solid?

[@ak5ogaming99]

Plz give me answer

[@adamost4831]

How can a rate = quantity + rate?

[@LearnChemE]

good question. In this case, "flow" is actually a rate as well.

[@nooralshaer3105]

dudeeee thanks a lot, that was amazing

[@Tonkiplis]

At about 7 minutes, you mention that the rate at which internal energy changes in the system is equal to the heat capacity * temperature difference.
What I remember from thermodynamics is that (dU/dT)v si equal to Cv and not Cp...
what I am missing? Is Cv=Cp for a solid?

[@LearnChemE]

Tonkiplis For a solid that does not expand or contract, Cp does indeed equal Cv.

[@Tonkiplis]

Tonkiplis but the volume of the solid is temperature dependent, no? Is this dependance neglected? Thanks for your answers

[@Tonkiplis]

Tonkiplis and would you know a book which states this equality, such that I can refer to?
Have a nice day!

[@LearnChemE]

Tonkiplis The volume change of a solid due to temperature is certainly negligible. I apologize for being ambiguous in my last response. Let me rewrite that: For a solid, which does not expand or contract, Cp does indeed equal Cv. (There will be minor exceptions to this rule for some unusual substances, but generally not in any temperature regions where we would be interested.)

[@mustafak4b]

You are amazing !

[@qwertasdfg1519]

thank you guy, it helped me)

[@chandrachudmishra2671]

Beautiful

[@zajec11]

Smooth and beautiful

[@jimmynaqvi3591]

I owe you a beer

[@hsoley]

I cant thank you enough!

[@MahmoudAhmed-lt1nv]

This is great ♡ !

[@myrontheoharakis9392]

THANK YOU!!

[@nissikasombwe7345]

Thanks a lot

[@puya1342]

awesome!

[@Inamullahkhan6294]

explained well but little bit faster.

[@SkyPirateU]

Hell's yeah !!

[@anurag4nov]

thanx a lot man :-)

[@calebgrant5851]

Very hard to take notes on a subject when the screencast does things that are impossible on paper: moving text, instantaneous writing, side scrolling, etc.

[@LearnChemE]

+James Grant Some people find it helpful to pause at certain spots or to rewind the screencast in such circumstances.

[@001nithin]

thanks a lot,,,,,, :)

[@chrisvl7352]

Thank you!!!

[@rafaanimir8820]

This channel is really amazing, thumbs up (y)